Question

hyperbolic motion: why picking a sign?

Answer 1

the metric needed to do this is (+,−,−,−)(+,−,−,−). We assume motion just in one direction so 4-velocity and 4-acceleration are respectively

uμ=(u0,u1,0,0)wμ=(w0,w1,0,0)uμ=(u0,u1,0,0)wμ=(w0,w1,0,0)

With wμwμ=−g2wμwμ=−g2

Now using the properties uμwμ=0uμwμ=0 and uμuμ=1uμuμ=1 we arrive at

(w1)2=±gu0−−−√

Answer 2

Explanation:

Hyperbolic Motion. By way of example, let's consider a rocket with proper length L = 0.8 light-years